Question

Nolan has a points card for a movie theater.• He receives 20 rewards points just for signing up.• He earns 2.5 points for each visit to the movie theater.• He needs at least 40 points for a free movie ticket.Write and solve an inequality which can be used to determine v, the number of visitsNolan can make to earn his first free movie ticket.Inequality:Submit Answer

Answer 1

Given:

Rewards for signing up is 20 points.

Reward for each visit to theater is 2.5 points.

Minimum required points to earn a free ticket is 40 points.

Here the reward for signing up is fixed points. But the reward point for visiting each theater varies depends on the number of visits.

Consider the number of visits as v.

Then, the above situation can be expressed in the form of linear equation as,

`20+2.5v\ge40`

Hence, the required equation of inequality is obtained.

On solving for v,

`\begin{gathered} 20+2.5v\ge40 \\ 2.5v\ge40-20 \\ 2.5v\ge20 \\ v\ge(20)/(2.5) \\ v\ge8 \end{gathered}`

Hence, Nolan should make atleast 8 visit to theater to earn his first free movie ticket.